【LOJ】#6436. 「PKUSC2018」神仙的遊戲
阿新 • • 發佈:2018-12-15
題解
感覺智商為0啊QAQ
顯然對於一個長度為\(len\)的border,每個點同餘\(n - len\)的部分必然相等
那麼我們求一個\(f[a]\)陣列,如果存在\(s[x] = 0\)且\(s[y] = 1\)且\(|x - y| = a\)
這個很好求,只要把0和1分別挑出來,NTT卷一下就好了
一個\(len\)合法,即它的\(n - len\)的倍數\(k\),\(f[k]\)都等於0
程式碼
#include <bits/stdc++.h> #define fi first #define se second #define pii pair<int,int> #define pdi pair<db,int> #define mp make_pair #define pb push_back #define enter putchar('\n') #define space putchar(' ') #define eps 1e-8 #define mo 974711 #define MAXN 500005 //#define ivorysi using namespace std; typedef long long int64; typedef double db; template<class T> void read(T &res) { res = 0;char c = getchar();T f = 1; while(c < '0' || c > '9') { if(c == '-') f = -1; c = getchar(); } while(c >= '0' && c <= '9') { res = res * 10 + c - '0'; c = getchar(); } res *= f; } template<class T> void out(T x) { if(x < 0) {x = -x;putchar('-');} if(x >= 10) { out(x / 10); } putchar('0' + x % 10); } const int MOD = 998244353,MAXL = (1 << 20); int W[MAXL + 5],f[MAXL + 5],g[MAXL + 5],N; char s[MAXN]; int inc(int a,int b) { return a + b >= MOD ? a + b - MOD : a + b; } int mul(int a,int b) { return 1LL * a * b % MOD; } int fpow(int x,int c) { int res = 1,t = x; while(c) { if(c & 1) res = mul(res,t); t = mul(t,t); c >>= 1; } return res; } void NTT(int *p,int len,int on) { for(int i = 1 , j = len >> 1 ; i < len - 1 ; ++i) { if(i < j) swap(p[i],p[j]); int k = (len >> 1); while(j >= k) { j -= k; k >>= 1; } j += k; } for(int h = 2 ; h <= len ; h <<= 1) { int wn = W[(MAXL + MAXL / h * on) % MAXL]; for(int k = 0 ; k < len ; k += h) { int w = 1; for(int j = k ; j < k + h / 2 ; ++j) { int u = p[j],t = mul(p[j + h / 2],w); p[j] = inc(u,t); p[j + h / 2] = inc(u,MOD - t); w = mul(w,wn); } } } if(on == -1) { int InvL = fpow(len,MOD - 2); for(int i = 0 ; i < len ; ++i) p[i] = mul(p[i],InvL); } } void Init() { W[0] = 1;W[1] = fpow(3,(MOD - 1) / MAXL); for(int i = 2 ; i < MAXL ; ++i) { W[i] = mul(W[i - 1],W[1]); } scanf("%s",s + 1); } void Solve() { int t = 1; N = strlen(s + 1); while(t <= 2 * N) t <<= 1; for(int i = 1 ; i <= N ; ++i) { f[i] = (s[i] == '1'); g[i] = (s[N - i + 1] == '0'); } NTT(f,t,1);NTT(g,t,1); for(int i = 0 ; i < t; ++i) f[i] = mul(f[i],g[i]); NTT(f,t,-1); int64 ans = 1LL * N * N; for(int i = 1 ; i < N ; ++i) { int t = i; bool flag = 0; while(t < N) { if(f[N - t + 1] || f[N + t + 1]) {flag = 1;break;} t += i; } if(!flag) ans ^= 1LL * (N - i) * (N - i); } out(ans);enter; } int main() { #ifdef ivorysi freopen("f1.in","r",stdin); #endif Init(); Solve(); }